Samuelj's Complex Plotter Fractals

// T is used for iteration count

float dist(vec2 p) {
  // returns distance from origin
  return sqrt((p.x * p.x) + (p.y * p.y));
}

vec2 cdot(vec2 i, vec2 j) {
  // returns the dot product of
  // two complex numbers, treating
  // them as vectors
  return vec2(i.x * j.x, i.y * j.y);
}

vec2 conj(vec2 p) {
  // conjugate of a complex number
  return vec2(p.x, -p.y);
}

vec2 cpow(vec2 value, float power)
{
  // courtesy of ChatGPT
  // does an imaginary to the power of a real.
  float r = length(value);
  float theta = atan(value.y, value.x);
  float r_pow = pow(r, power);
  float theta_pow = theta * power;
  return vec2(r_pow * cos(theta_pow), r_pow * sin(theta_pow));
}

vec2 mapping(vec2 z) {
  vec2 c = z;
  vec2 p = vec2(a.x, b.x);

  for (float i = 0.0; i < 100.0; i+=1.0) {
    if(i > t.x) {break;}

    /// modify THIS line ///
    z = cmul(z, z) + c;

  }

  // DISTANCE based coloring
  // (needs variable h, range 0-4)
  //z = cmul(vec2(pow(dist(z)+0.5, 8.0), 0.0), cpow(vec2(0, 1), h.x));

  // INCREASE CONTRAST
  //z = vec2(pow(abs(z.x)+0.5, 8.0)*sign(z.x), pow(abs(z.y)+0.5, 8.0)*sign(z.y));

  return z;
}

// personal favorites:
// z = cdiv(vec2(z.x, c.y), cdiv(cmul(z, z), cdot(c, c)) + cmul(c, p));